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Theorem pm3.31 445
Description: Theorem *3.31 (Imp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)
Assertion
Ref Expression
pm3.31  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  /\  ps )  ->  ch ) )

Proof of Theorem pm3.31
StepHypRef Expression
1 id 22 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ph  ->  ( ps  ->  ch ) ) )
21impd 431 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  /\  ps )  ->  ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  impexp  446  imp5a  598  issref  5320  stoweidlem17  29961  trsbc  31580  3impexpVD  31925  trsbcVD  31946  19.41rgVD  31971
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